何度も言ってますけど = "I'm saying it over and over, but..."
ボクは寒いのは本当に苦手なのです。 = "I'm one of those who is really bad with the cold."
暖房を入れると = "If I turn on the heater..."
頭がボ〜〜とするし, = "I get tired and lazy,"
切ると = "if I turn it off..."
いきなり手がかじかんで = "my hands suddenly grow numb from the cold,"
ペンをうまく持てないし... = "and I can't even use a pen properly..."

You said you didn't understand how things were being said. After looking at the above, is there something specific you don't grasp?